Zero Product Rule for solving equations
In this article, I will explain how to use the zero product rule to solve equations like this:
To understand the article, you’ll need to be comfortable with the following:
- Simple rule of multiplication
- How to solve linear equations
- How to factor polynomials
If you’d like an article on any of these topics, please leave a comment below. I’d recommend reading Beginning And Intermediate Algebra by Tyler Wallace to learn more about the Zero Product Rule
Let’s begin with a simple rule of multiplication, if we multiply a number by zero the answer is zero. For example, if we take the number 5 and multiply it by zero we will get zero i.e. 5 x 0 = 0.
If we then see that the multiplication of numbers is equal to zero, we should know that one of the numbers was zero i.e.
Zero Product Rule: ab = 0 then a = 0 or b = 0
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Okay this is cool to know but how would this apply to an equation like the one shown in the beginning of the article? It doesn’t have any multiplication, it just has terms being added to each other.
Luckily we also know that we can take a polynomial and reverse it to the items that were multiplied to get it i.e. we can get the factors of the polynomial as shown below:
Using the zero product rule we know the following:
The example above shows us how we can combine all of our knowledge to solve the equation! It’s amazing how the different knowledge we have has come together to solve a new kind of problem.
A summary of the zero product rule for solving equations:
- The equation we are solving has to equal zero
- We need to factor the polynomial
If we are in a case where the equation is not equal to zero, we will need to first make it equal to zero to use the zero product rule as shown below:
Thanks for reading the article! Leave any questions you might have in the comments. If you have any suggestions on other topics to write articles on I’d love to hear them!
